NAT'L INST. OF STAND & TECH

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* NBS TECHNICAL NOTE 1060

Reference

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SJt ^kutcorL ft/ore, /OGO

,- * j> Measurement of Multimode Optical

Fiber Attenuation

R. L Gallawa

G. E. Chamberlain

G. W. Day

D. L Franzen

M. Young

Electromagnetic Technology Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

e

**rcsO*^

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

NBS RESEARCH INFORMATO

CENTS.7

?

I co

/Oo . 10b

"*3

June 1983
National Bureau of Standards Technical Note 1060

Nat. Bur. Stand. (U.S.), Tech. Note 1060, 52 pages (June 1983)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1983

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402

Price $4.00

(Add 25 percent for other than U.S. mailing)
CONTENTS

Page

1. Introduction 1 2. Launch Conditions 5 2.1 Phase Space 5 2.1.1 A Summary of Phase Space Concepts 14 2.2 LPS Launch 16 2.3 Mode Filter Launch 18

3. Component and System Variabilities 22 3.1 Spot Size and Launch Numerical Aperture 22 3.2 Mode Filter Qualification 28

3.3 Component Linearity 31 3.4 System Linearity 31 3.5 System Noise 32 3.6 Detector Uniformity 33 3.7 Measurement Procedure 33 3.8 Some Results 37

4. Measurement Comparisons and Results 37 4.1 Participants and Instructions 37 4.2 Comparison Results 38 4.3 Attenuation Measurements in High-DMA Fibers 41 4.4 Summary of Interlaboratory Comparisons 43

5. References 43

Appendix A. Mode Volume and Limited Phase Space 45

m

Measurement of Multimode Optical Fiber Attenuation

R. L. Gallawa, G. E. Chamberlain, G. W. Day,

D. L. Franzen, and M. Young*

National Bureau of Standards

Boulder, Colorado 80303

This document is one of a series which describes optical fiber measurement

capabilities at the National Bureau of Standards. We concentrate here on the measurement

of attenuation of multimode, telecommunication-grade fibers for the wavelength range of

850 nm to 1300 nm. The document begins by discussing the need for restricted launch

conditions, the most fundamental and crucial aspect of precise attenuation measurements.

The limited phase space launch (also called the beam optics launch) and the mode filter

launch are discussed. Attention then turns to the practical matter of ensuring that the

conditions of the restricted launch are met. Discussions of system noise and system

linearity are also included. The document describes measurement procedure and results

obtained in the laboratory using three typical fibers. Results are presented for the two

wavelengths of current interest: 850 nm and 1300 nm. The procedures are applicable to any wavelength, however. The document touches briefly on the matter of monomode fibers.

Finally, a summary of the results from an interlaboratory comparison are presented to give

perspective to the stability of a fiber subjected to handling and shipping.

Key words: attenuation; attenuation measurement; fiber measurement; optical fibers;

optical waveguides.

1. Introduction

Two operational parameters are basic to the utility of any transmission line: attenuation and

bandwidth. These two determine repeater spacing and ultimate cost of a telecommunication network.

Both must be characterized because either attenuation or bandwidth may limit the range-bandwidth

product of a communication link; the range-bandwidth product is the most frequently used measure of

performance and cost. Full exploitation of system components depends on an understanding of which

parameter (bandwidth or attenuation) is restricting system capability.

The techniques described in this document are applicable to all wavelengths of interest for

telecommunications. The measurements reported on, however, were done at only 850 nm and 1300 nm. The

system uses an incandescent strip filament light source in conjunction with interference filters for

wavelength selection. Thus, it is amenable to measurement at discrete wavelengths.

We restrict attention to telecommunications-quality graded-index multimode fibers. Such fibers

have a nominally 50 pm core diameter and the refractive index profile is carefully controlled.

Usually the profile is nearly parabolic, yielding high bandwidth. The loss in telecommunication-grade

fibers is as low as practical. Fibers used in short-distance applications or LAN (local area networks) are frequently large core fibers and often have a step index profile. The attenuation is less important than it is for long haul fibers. Even if the fibers used in the two applications (long

and short distances) were identical, the philosophy behind the measurement technique would undoubtedly

*Electromagnetic Technology Division, National Engineering Laboratory.
be different in the two cases. For long distance fibers, the measured value of attenuation should be

indicative of the attenuation experienced in a long link. Likewise, the attenuation measured for a short distance fiber should be representative of the attenuation experienced in a typical short

distance application. The modal power distribution at launch is important to the measured value of

attenuation in each case.

The philosophy of improving measurement precision by restricting the launch is intimately

related to the excitation of high-loss modes, including leaky modes. The concept is distinctly

different in graded-index and step-index fibers. By uniformly illuminating the fiber core using a limited launch numerical aperture, one avoids the excitation of high-order and leaky modes of a stepindex fiber. This is not true when the fiber has a graded refractive index because the local

numerical aperture of the fiber is a function of radial position.

A launch condition that works well for step-index fibers may not work well for graded-index

ones. The converse is also true: a launch condition that yields usable results for a graded-index

fiber may not be the most suitable one for step-index fibers. The reported attenuation must be

meaningful in the context of its application. Short-haul links using LED sources are not considered

in this document. We are concerned here with the characterization of fibers in a way that will be useful in predicting the performance of a telecommunication link, which may include concatenated

fibers.

Monomode fibers, though not considered in this document, are important in high capacity, long

haul systems, where attenuation is more likely to be the limiting parameter in system design. Launch

conditions are simpler for monomode fibers since only the fundamental mode will propagate. A mode

filter or limited launch numerical aperture is therefore not necessary. The fiber will support two

orthogonal polarization states and this may be a source of inaccuracy if the light is polarized.

Coupling between the polarization states of the fiber may be difficult to control. Furthermore, the

attenuation coefficient is different for the two states. The problems associated with the

birefringence of the fiber are especially important in systems that are phase sensitive. A meaningful

characterization of the monomode fiber is difficult in that case.

Fiber attenuation is the diminution of average optical power, measured in decibels. The rate of

diminution, with respect to distance, is known as the attenuation coefficient for the fiber, usually

denoted by a, and is specified in decibels/kilometer. If a is constant, the attenuation of a length L of fiber is

aL(dB) = -10 log [P(L)/P(0)L (1-1)

where P(L) is the power at distance L from the reference position where the power is P(0) and log

indicates the common logarithm. In practice, the attenuation coefficient varies with distance and

operating wavelength, X. The parameter of interest, then, is the average attenuation of the fiber, as found from eq (1-1), where

L /

. a(z,A)dz
The obvious method of measuring attenuation, then, is as follows: power reaching a detector through

two different lengths of fiber (L , L ) is measured for the operating wavelength of interest. The

average attenuation coefficient is

10

P(L »» <*> - l^r; "» pJl? • (1 - 3)

In this form, attenuation is positive if L > L .

For graded-index multimode fibers, the utility of such a measurement depends on how power was launched into the fiber. The transmitted power resides in a finite number of modes, and different

modes have different attenuation coefficients. Thus, the measured average attenuation of a multimode

fiber depends on the relative amount of power in each mode. At launch, the relative power depends on launch conditions. A small LD (laser diode) may launch its power into the center region of the fiber

but overfill the fiber numerical aperture. An LED (light-emitting diode) has a broad angular radiation pattern and large size so it excites all modes more or less uniformly. Clearly, the attenuation

measured using an LED source is different from that measured using an LD. This difference in attenuation disappears after the fiber reaches the steady-state or condition of equilibrium modal

power distribution, in which case the relative power in the various modes is independent of length.

Thus, the modal power distribution at the output is independent of the modal power distribution at input. The equilibrium condition is achieved beyond a certain propagation distance called the

equilibrium length. The condition is reached after the high-loss modes have been attenuated or coupled into modes which have less attenuation. In the steady-state condition, intermodal coupling is

in equilibrium, so power coupled from one mode to the others is just compensated by differential

attenuation and power coupled in the opposite direction. The effect of an equilibrium modal power

distribution is shown in figure 1-1 (after ref. 1) which shows the result of length-dependent

measurements on a 4 km length of parabolic profile fiber at 800 nm and 1060 nm. The launch numerical

aperture is 0.10 in each case. Steady state appears to be reached after about 2 km. For shorter

lengths, the attenuation coefficient is higher than the steady-state value; this can be attributed to the presence of high-loss modes. The slope of the curve at any point gives the local attenuation

coefficient. The slope (attenuation coefficient) in the first kilometer of fiber is significantly

higher than in the fourth kilometer of the same fiber. This figure illustrates, then, the need for

launch conditions which create the desired power distribution and, hence, lead to attenuation values

that are typical of long fibers.

More recent results show a similar trend but the distance required to reach steady state is considerably reduced [2]. Recent data confirm that differential mode attenuation is considerably less

today than it was just a few years ago. Furthermore, differential mode attenuation is a function of

operating wavelength, so the distance required to reach steady state changes with a change in

operating wavelength.

The two launch conditions used in this report are the LPS (limited phase space) launch (also

called the beam optics launch) and the mode filter launch. In the first, the launch spot size and the

launch numerical aperture are adjusted to be, respectively, 70 percent of the fiber core size and 70 percent of the fiber numerical aperture. The condition is therefore also referred to as the 70/70

launch condition. The LPS launch apparatus is more complicated than the mode filter launch because

the apparatus must allow for independent adjustment of launch spot size and launch angle. The product

of launch spot size and launch angle is related to phase space volume, discussed in section 2.1.
6.3 dB/km

X- 800 nm

5.1 dB/km

20

4.4 dB/km

1 2 3 Fiber Length, km

Figure 1-1. Loss in a 4 km length of parabolic profile

fiber. Launch NA = 0.1 in each case. After

reference 1.

The mode filter launch calls for launch spot size and launch angle larger than fiber core size

and fiber numerical aperture. The launch optics can therefore be rather simple. The overfilled fiber

is subjected to a filter, the purpose of which is to establish a modal power distribution that

approximates the modal power distribution at the end of a long fiber without the filter. The mode

filter is deemed appropriate if a short length of the test fiber which is subjected to the filter

produces a far-field radiation pattern that is similar (within tolerance) to that of the long test fiber without the filter.

Details on the two launch conditions are given in section 2.

The problems discussed here are not applicable to monomode fibers, where the optical size of the

fiber is so small that only a single mode can propagate.

Since the strength of intermodal coupling influences the attenuation of the fiber, the environment can affect the measured attenuation. The loss value assigned to an uncabled fiber may not be appropriate to the cabled fiber. Likewise, the loss of an uncabled fiber on a spool depends on how

tightly the fiber is wrapped around the spool.

For purposes of fiber specification (i.e., for purposes of trade and commerce) it is important

that the attenuation assigned to a fiber be of practical use. When fibers are concatenated, the

attenuation of the resulting link should be predictable from the specified attenuation of individual

fiber sections. That is the crux of the attenuation measurement problem.

In this report, we discuss specific details of a meaningful measurement technique. Before proceeding, however, we note that the mode coupling discussed above has a beneficial effect on fiber

bandwidth as well. Different modes have different phase and group velocities, as well as different

attenuations. The duration of a pulse increases as it propagates in a multimode fiber. The increased

duration results from different group velocities of the different modes. Initially, pulse duration

usually increases linearly with distance, but for lengths exceeding the equilibrium length, the pulse

duration may increase more slowly with distance, approaching L

1 ' 2 variation in some cases [3,4].
100

10

r eo o1 40 cV

< 20J

CD

12 3 4 6 6 7 Launch Angle, degrees

Figure 2-1. Attenuation coefficient as a function of input plane wave angle at 632.8 nm (after ref. 5).

Mode Number, m/M

Figure 2-2. Symbolic representation of 0.28 NA fiber waveguide attenuation at 800

nm as a function of mode number.

Mode number was altered by changing

launch spot position but not launch

angle. Launch angle is (after

ref. 6).

2. Launch Conditions

That different modes have different attenuation coefficients is intuitive. Figures 2-1 and 2-2

[5,6] give experimental evidence to support the allegation. Figure 2-1 shows the attenuation coefficient as a function of input launch angle for a step-index fiber at 6328 nm. The high-order modes

associated with the steep input angles show a very high attenuation per unit length. In contrast, the

low-order rays have fairly uniform attenuation. Clearly then, the input launch condition plays an important role in the measured attenuation. Figure 2-2 is symbolic of the attenuation coefficient as

a function of normalized mode number at 800 nm for a graded fiber having 0.28 NA. Both scattering and

absorptive loss have been accounted for in this curve [6]. In the figure, M is the mode volume of the

fiber or the total number of modes the fiber will support (cf. appendix A), m is the counting index

that identifies the mode number.

A complete description of modal properties and how those properties influence fiber attenuation

is beyond the scope of this manuscript. The reader is referred to the references for additional

details [7]. For our purposes, we concentrate on the launch conditions and how those conditions

influence the excitation of various modes. To that end, we digress briefly to discuss the concept of

phase space. That concept is fundamental to one of the two launch conditions discussed in this document. Those conditions are discussed later in this section.

2.1 Phase Space

The concept of phase space is basic to the limited phase space launch condition. In this

section, we give some basic definitions and connecting relationships that lend credence to the proposition that the LPS launch is a reasonable one to use. The reader who is not interested in these

connecting relationships can skip directly to section 2.2 or he may pause to read the summary paragraphs in section 2.1.1.
Figure 2-3. A typical light ray and angles in a rectan- gular coordinate system.

Phase space and its relationship to the problem of coupling optical energy to and from a source

is understood by noting first that a light ray has "momentum" which depends on its position and direction. If the optical axis is the z-axis of a rectangular (x,y,z) coordinate system, the momentum of

the ray depends on x, y, dx/ds and dy/ds, where x,y is its location and ds is its incremental distance

along the ray path. In particular, the momenta in the x and y directions are

P

x

= n dx/ds, (2-la)

p y

= n dy/ds, (2-lb)

where n is the refractive index at x, y and may be a function of position. Figure 2-3 shows a typical

light ray and its angle with respect to the axial (z) direction. In this case,

pK = n sin a,

x (2-2a)

n sin 3. >2b)

The physical state of a ray is completely specified by the four variables x, y, p x

, p

y

. These four

variables define a four-dimensional space called the phase space. The position of a ray in phase

space has a one-to-one relationship with its trajectory in physical space.

The power coupled into a fiber mode depends on the trajectory of the launch ray so it is not sur- prising that these concepts should be encountered in a discussion of restricted launch conditions.

Indeed, the efficiency of coupling between fibers or between a fiber and a terminal device (e.g., a light source) is characterized by the phase space match. The conservation of radiance, for example,

is a manifestation of this concept, as will be seen below. For the purpose of measuring fiber attenuation, we seek to establish a launch condition for which the phase space matches the phase space

desired in the fiber.
Figure 2-4. Illustrating angles and areas used

to discuss phase space.

Optical coupling depends on the density of points in phase space. Each ray in a bundle of rays

is represented by a point in phase space, and the collection of rays in the bundle corresponds to a volume (denoted ty) in phase space. As the ray bundle moves through physical space, the direction and

location of the rays change; this corresponds to a change in location of the various points in phase

space. The density of points p is the number of points per phase space volume. One form of

Liouville's theorem [8] demands that neither the density of points in phase space nor the phase space

volume can change with axial direction; i.e., dp/dz = 0, di>/dz = 0.

Normally, and not unexpectedly, the density is defined in terms of the incremental power, dP, in an increment of phase space volume dty.

dP/d*. '2-3'

This equation shows that radiance is proportional to density, as will be seen. The total power (or,

equi valently , the total number of rays) is found by integrating over phase space:

/ dP = Jpd* = /p dxdydp dp . X J '2-4'

Figure 2-4 shows the relationship between the differential volume element in phase space and the

product of differential area and differential solid angle in physical space. The area dxdy is normal

to the z-axis and could represent a source radiating into the right-half plane. The figure shows that

pr

= n sin a,

x >5a)

p = n cos a si n y = n si n 3, :2-5b'

dpr

= n cos a da,

x

dp = n cos a cos y dy = n cos g df

;2-5c:

:2-5d:
The differential volume in the plane z = is

d\jj = dxdy n 2 cos 2 a cosy da dy. (2-6)

The projection of the source normal to the ray is

da = dxdy cosa cosy = rda r cos a dy. (2-7)

The solid angle encompassed by da is therefore

dQ = da/r 2 = cos a dady. (2-8)

Thus,

d\p = n 2 dxdy dfi cosa cosy = n 2 da dfi, (2-9)

where da is normal to the ray.

This important connecting relationship between phase space and the product of area and solid

angle is fundamental to one of the launch conditions used to measure attenuation. The relationship is

a manifestation of the conservation of radiance, since

dP dP L ,o ^r,^ p = -r = ~oz—j- = -9 » 2-10)

dip n

2 da dfi n2 v '

where radiance L is, by definition,

L-* (2-11)

da dn

The requirement dp/dz = is equivalent, then, to the conservation of radiance:

^ (^ = 0. (2-12)

The concept of a LPS (limited-phase space) launch is based on eq (2-9) and the requirement that

only bound modes having "reasonable" loss values should be launched when measuring attenuation. This

leads to measured values that are reproducible (precise) and more or less independent of the person

who made the measurement. The LPS launch calls for a launch spot size equal to 70 percent (actually,

/0.5) of the fiber core diameter and a launch numerical aperture equal to 70 percent (actually, /0.5)

of the fiber numerical aperture [9]. The reason for this selection is related to the power-accepting

properties of a fiber and the concept of fiber NA (numerical aperture). To examine the relationship

between fiber NA and phase space, consider the following.

The concept of fiber NA becomes slightly complex when leaky rays are considered [10]. A leaky

ray (or, correspondingly, a leaky mode) is one for which geometric optics would predict total internal reflection at the core-cladding boundary, but which suffers loss by virtue of the curved core boundary. Specifically, a leaky ray is a ray located at radial position r and having direction such

that
Cladding

<n 2

>

Figure 2-5. A typical light ray and

angles in a fiber.

-> , * o , ^ • i i ^ n2 (r) - n2 (a)

n2(r) - n2(i)<5in2l(r)< i-wcos4r ;2-13a)

where e(r) is the angle the ray makes with the waveguide axis, n(r) is the r-dependent refractive

index, a is the core radius, and <)>(r) is the azimuthal angle of the projection of the ray on the

transverse plane [11]. A bound ray is one for which

< sin 2 (e) < n

2 (r) - n2 (a). >13b)

Figure 2-5 shows a ray in a fiber; the angles appearing in eq (2-13) are shown, as are other angles,

as well as the radial, azimuthal, and axial components of the wave vector k (k

p

, k,, k

z = p); k is the wave number in free space. Skew rays correspond to <}> < tt/2 ; meridional rays correspond to

<j> = it/2. Meridional rays always traverse the fiber axis while skew rays never do.

If leaky rays are included, the local numerical aperture of a fiber (which determines whether or not an incident ray is accepted) is defined as 1/2

NA = (NA]

1 r/a;

1 - (r/a) 2 cos 2

<j> :2-i4'
where

(MA) = (n2 - n

2

) 1 ^ (2-15)

1 2

and g is the power-law profile parameter; i.e., it is assumed that

n(r) = n [1 - 2A(r/a) 9

] 1/2, (2-16)

where n is the refractive index at r = 0; A is the contrast, specifying the difference between n(0)

and n(a) = n_. If $

- it/2,

m

U=«/2

= (NA)

o

Cl " ( p / a ) 9

] 1/2

- (2" 17 )

The power accepted by the fiber at any point on the core is proportional to the square of the

numerical aperture. The equation for (NA) 2 is the equation of an ellipse, which degenerates to a circle at r = 0. The ellipse has semi-major axis

1 - (r/a)V /2

'o

L l - (r/a) on. : i ; - ym

> r, (2-18)

and semi -mi nor axis

(NA)

Q

[1 - (r/a) g

] 1/2

. (2-19)

The area of the ellipse is proportional to the product of these two axes:

Area = tt(NA) 2

l ' (r/a)

(2-20)

° [1 - (r/a)*]

1 ^

At r = 0, the circle that describes NA has area tt(NA) 2

. The ratio of the two areas is the ratio of

o power accepted by the fiber at radius r to that accepted at r = 0:

P(r) 1 - (r/a) g

P(0) ' [1 - (r/a) 2

] 1/2

'

This result can also be obtained from the phase space representation using the notation of figure

2-5. For the circular cylindrical system

di|> = dA sine cose de d<(», (2-22a)

where dA is the incremental area on the fiber core. The fiber near field, as given in eq (2-21), is obtained by integrating di|j/dA over all angles:

tt/2 9

c

(r,<fr)

/ d<|> / sin e cos e de

fill = ° ^— (2-22b)

P(0) tt/2 6 (O.ir/2)

V

'

/ d<() / sin 9 cos 9 de

o o

10
where in the numerator,

c

, n 2q ,„ x \ _

n

2 (r) - n 2

a sin z

9 (r,4>) =-

? =—-, c 1 - (r/a) z cos z $

(2-22c)

and in the denominator,

sin 29 (0,ir/2) = n

2 (0) - n 2 (a) = n 2 - n< (2-22d)

Telecommunication-grade multimode fibers have parabolic (or nearly parabolic) profiles, so g = 2. In that case, the near field becomes

If leaky rays are excluded,

P(r)

P(0)

P(r)

P(0)

•1 - (r/a) 2

. (2-23a;

1 - (r/a) 2 . (2-23b;

The far field of the fiber can be obtained similarly from eq (2-22b) by again assuming all modes

are equally excited and g

= 2:

pm R(0,*) ir/2 M-1J / RdR d<t>,

where R = r/a and, for leaky and guided rays,

R

2 (e,4,) =

When leaky rays are excluded,

1 - [sine/(NA) ]

1 - [sine/(NA) ] 2 cos 2

<(.

(2-24a;

R

2

(e,<(») = 1 - [sine/(NA)

o ]\ (2-24b;

For g = 2, the fiber far field is

for bound modes only and

P(e)

P(0]

= 1 -sine ^2 (na;

(e) h f _P(e sine >2,l/2

p

:2-25a'

>25b)

when leaky rays are included.

The LPS launch calls for a uniform launch spot of specified size and specified launch angle.

These conditions can be put into perspective by using the concepts discussed here. Consider a uniform

spot of diameter rQfocused onto the end of a fiber core having diameter a. The launch angle with

11
respect to the fiber axis is e Q

. The power that the spot launches into the fiber can be found using

eqs (2-4), (2-9), and (2-10). The radial and azimuthal coordinate variables in the plane of the fiber

end face (or spot) are taken to be r, £. Incremental area da is therefore r dr d£. The total power

coupled from the spot to the fiber is re 2tt 2tt

P ( ro'V =

/ / / /

L rdrd ^ sine cos9 ded<f> (2-26a) 000

where L is the (uniform) radiance of the launch spot and sine ded<|> is the solid angle into which da

launches power (cf. fig. 2-5, but r and 5 are not shown in that figure), da cose is the component of

da that is normal to the ray direction. We suppose that the launch spot radiance is independent of 5,

yielding

P ( r o'

9 ) = L o

(irr o )2sir,2 V ( 2

" 26b )

In deriving this equation, we have assumed that the fiber accepts all rays incident from the launch

spot. The validity of this assumption depends on the refractive index profile of the fiber. If the

fiber has a parabolic profile, the assumption will hold if r Q

and e Q are related thus:

(r

Q

/a)

2 + [sine

o /(NA)

o

] 2

< 1, (2-26c)

with (NA) defined in eq (2-15).

Additional insight is had by normalizing eq (2-26b), using R

Q

= rQ /a:

sine

12

P ( R o>

e o>

= KR otTNAfJ • < 2 " 26d )

v 'o

where K is a constant that depends on the strength of source. The LPS launch is based on a meaningful

choice of RQ

and e . This is discussed further below.

Equation (2-26d) is a measure of how well the phase space of the spot matches that of the

fiber. In this sense, it gives the expected coupling efficiency between the two but without including

reflection loss. This will be seen in discussing figure 2-6c, which is a plot of eq (2-26d).

Equation (2-26d) is fundamental to the LPS launch, since it contains only the launch spot parameters

and the fiber parameters.

Figures 2-6a, b, c, and d are plots of eqs (2-13), (2-23), (2-25), and 2-26d) subject to

eq (2-26c) for g = 2. They are included to help explain the LPS launch. Note first that the straight

diagonal line between (0,1) and (1,0) in the figures is the line y

2 = 1 - x2

, where y

2 is the ordinate

and x

2 is the abscissa. The region below that line represents the region of bound modes. Figure 2-6a

shows that if the launch spot size is 70 percent of the fiber core size and the launch numerical

aperture is 70 percent of the fiber numerical aperture, the phase space excited in the fiber is shown

by the square in the lower left corner of the figure. The power launched is given by eq (2-26d) with

R

2 = 0.5 and [si nQ /(NA) ] 2

= 0.5. No leaky modes are excited.

12
(a

2

v

? 0.5

R£ or [Sinfl» /(NA) ]'

(c) (d)

Figure 2-6. (a) The phase space of a graded-i ndex fiber. Darkened area shows the phase space excited

by the LPS launch.

(b) The normalized near field of a parabolic profile fiber (g = 2).

(c) The normalized far field of a parabolic profile fiber (g = 2).

(d) Normalized power launched into a parabolic profile fiber (g = 2) under the condition

that R Q and sine

Q are chosen so no leaky modes are excited but that maximum power is coupled into the fiber. Uniform launch condition.

Holmes [9] has discussed the launch condition described here. He defined the EMV (effective mode

volume) of a fiber in terms of the far-field and the near-field intensity distributions of the

fiber. EMV is the square of the product of the normalized full width at half maximum (FWHM) of the

near-field distribution and the normalized sine of the half width at half maximum (HWHM) of the farfield radiation pattern. Figures 2-6b and 2-6c relate this definition of EMV to the LPS launch

condition illustrated in figure 2-6a. If leaky rays are excited, the near field and the far field

will reveal this. Defining EMV in terms of the far field and the near field is thus obviously related

to the modal power distribution, as seen from the figures.

13
EMV is a convenient device and has proved to be useful in predicting steady-state conditions of

the fiber. Once the modal power distribution of a fiber is in equilibrium, the EMV as measured at the

fiber output is independent of fiber length; this is the condition sought when predicting attenuation

of concatenated links. The EMV at the input of a fiber depends on launch spot size and launch

numerical aperture as shown in the figures.

The concept of EMV is helpful and its use led to a useful launch condition. Recent work

demonstrates the complexity of the problem, however, and EMV clearly is not sufficient to circumscribe

the variabilities in attenuation measurements. A comparison of several filters and/or mode mixers

shows that each has its limitation but fortunately the fiber attenuation is relatively insensitive to

the fine details of launched modal power distribution [12,13],

Figure 2-6d relates the 70-70 launch condition to power launched under the restriction that spot

size and launch numerical aperture are chosen so no leaky modes are excited but that power coupled

into the fiber is maximum. This maximum power condition is not the primary reason for selecting the

70-70 launch condition. It does represent a happy coincidence, however.

Figure 2-7 [14] further illustrates the reason for the limited launch. The figure gives

attenuation along the vertical axis with launch variables in the horizontal plane. The measured

attenuation depends on how effectively various modes are excited. If the fiber core and numerical

aperture are fully filled at launch, attenuation is skewed by the high-loss modes, giving results that

would not be useful in predicting the loss in a system of several kilometers length.

2.1.1 A Summary of Phase Space Concepts

The definitions and connecting relationships given above form the basis of fundamental and

important concepts in optical coupling, including the coupling of light energy between a source and a fiber. Phase space is a four-dimensional space that is defined in terms of geometrical optics and

light rays. Two of the four dimensions are associated with the momentum of a ray [eq (2-1)] and the

other two are associated with the ray's spatial position. Each point in the four-dimensional space

has a one-to-one relationship to the ray's position in space and its direction (or momentum). This is

important because a ray enters a fiber at a point in space (on the fiber core) with a momentum

determined by its angle with respect to the fiber axis [cf. eq (2-2)].

Attenuation,

dB/km

k

(sjn£\2

\sin0r /

Region of LPS Launch

Figure 2-7. Attenuation as a function of ray parameters (after ref. 14).

14
The ray is bent as it passes from air into the fiber core according to Snell's law. The bending

can be described in terms of phase space by invoking the concept of the density of points in phase

space, denoted above by p. Neither the density of points nor the volume enclosing a fixed number of

points in phase space can change with z, the axial coordinate. Snell's law is a direct result of this

conservation principle. The conservation of density (p) and of volume (<|>) is a manifestation of

Liouville's theorem in statistical mechanics. The conservation of radiance is a consequence of these

conservation principles [see eq (2-12)].

Equation (2-9) shows that incremental volume in phase space is the product of area, solid angle,

and the square of refractive index. [The refractive index is squared because the angle is two dimensional (solid).] It is precisely this product that is controlled in the LPS launch. The product

is conserved in going from air to fiber core. The product is also the determinant of power launched

into the fiber. That is the thrust of eqs (2-13) to (2-26), as illustrated in figures 2-6(a) to 2-6(d).

Equation (2-26a), when used in conjunction with figure 2-6(a), can be used to deduce power

coupled into a fiber under several conditions. When a uniform source is assumed, the calculation can

be done easily in closed form. The figure helps in defining limits of integration. In particular, if

a spatially uniform light spot of radius r is focused onto the end of the fiber, the total power

coupled into the fiber (neglecting reflection losses) is

r 6 2tt O

P = 2it / rdr / / sin 9 cos 6 de d<j>,

where e o is the limiting value of 9; several values of 9 Q and rQ

will now be considered.

If the fiber is filled, r Q

= a, 9 Q= 9 C as given in eq (2-22c). The corresponding value of P will be referred to as PT0T . For the LPS launch, sin 2

9 = (NA) 2 /2 and rQ

= a//2 (cf. fig. (2-6a)).

The corresponding power launched will be referred to as P|_ps« The power coupled into guided modes, to the exclusion of leaky modes (referred to below as P

q

), is found by taking sin 2

9 Q

= (NA) 2 [1 - (r/a) 2

] and rQ

= a. To complete the picture, we will refer to P

Q

- P|_p$ as 2P

d

. The region outside the

shaded square but below the straight diagonal line in figure 2-6(a) represents the power 2P^. Finally, the amount of power in the leaky modes (P^) is P^ = Pygj - P_. The following relationships

are obtained from the integration, assuming a parabolic fiber with uniform mode excitation.

Pg/P* = 3, (2-27a)

VP T0T = 3/4 ' ( 2 ' 27b ) VP T0T = 1/4 > ( 2 " 27c )

P LPS/ P T0T =3/ 8 ' 2 " 27d )

P d /P Lps

= 1/2. (2-27e)

These ratios will be used later.

15
Equation (2-26d) gives the power coupled into a parabolic profile fiber as a function of launch

spot size and launch angle. It is again the product of area and solid angle that is the determinant

of power launched. The equation shows that launching power is a matter of matching the phase space of

the source to the phase space of the fiber. Only the phase space of each (aside from a multiplying

constant) appears in the equation. The maximum value of the right hand side is K and that obtains

when the phase space of the source equals that of the fiber; i.e., the fiber is filled and all bound

modes are excited. In that case, RQ

= 1 and sineQ= (NA)

Q

.

The equations reveal an interesting picture of power coupled into the bound modes of a parabolic

fiber. If launch angle and launch spot size are independently adjusted so only bound modes are excited, then maximum power is coupled into the fiber when launch spot diameter is 70 percent of core diameter and launch numerical aperture is 70 percent of fiber numerical aperture, provided the launch

spot is in focus and exactly centered on the fiber core.

Finally, the connecting relationships and figure 2-6 lead to what has been called the EVM (effective mode volume) of a fiber [9]. EMV is defined as the square of the product of the full width

at half maximum of the near-field pattern and the half width at half maximum of the far-field

pattern. That this is so is discussed above. Thus, the 70/70 launch condition is based on both the

near field and the far field of the fiber. The mode filter launch, described later, is based only on the far-field pattern of the fiber. The question of equivalence of the methods arises naturally,

then. The question cannot be answered definitely but some intuitive arguments in this regard are given later.

2.2 LPS Launch

Figure 2-8 is a block diagram of the system used to control launch spot size and launch numerical

aperture independently, in accordance with the requirements of the LPS technique. The method is

sometimes referred to as the beam optics method of launch.

The light source is a tungsten strip lamp powered by a regulated power supply to maintain

stability during the measurement. The strip lamp is preferable to coiled filament lamps because it produces a spatially uniform spot. The lens L converts the diverging beam to a beam of parallel rays

that pass through the interference filter for wavelength selection. The filters have a 10 nm spectral

width. The wheel that houses the several filters allows white light as one option; this option can be

used for alignment, as occasionally required. Lens L focuses the beam onto the aperture A , called

the source aperture, which is imaged onto the specimen,

launch spot size.

The size of A can be changed to adjust the

INTERFERENCE FITER

POWER

MONITOR

APERTURE | APERTURE

*1 f

A 2

D

LIGHT CHOPPER

Figure 2-8. Block diagram of attenuation measurement system. The system allows launch spot size and

launch numerical aperture to be controlled independently.

16
The beamsplitter shown in the figure serves a dual purpose. First, the arm marked power monitor

goes to a reference detector which monitors the stability of the light source. Correction can be made

in the final results if the output light power drifts during measurement. Experience has shown that

with a stabilized power source for the lamp, correction is almost never required and measurements are often made without the monitor arm activated. The computer program that controls data acquisition

allows the operator to monitor the source or not, as he sees fit. The beamsplitter also allows viewing the fiber end with the vidicon.

Aperture A controls the launch numerical aperture by restricting the beam angle. Thus, A and

A must both be adjustable, in accordance with the needs of the LPS launch.

The magnification (m < 1) introduced by the optics between A and the fiber end must be known.

The spot size on the fiber end is determined from m and the size of A . The launch spot size (A|_) is:

A. = A (£/£)= mA , L l 3 l

where l. is the distance from L to the image plane and i is the distance from A to L . Dimensions

are not accurately known so m is determined by measurement. A pinhole detector (small compared to expected spot size) scans the image plane of L to measure launch spot size for a known size of aperture A . Magnification is then calculated. In a similar manner, the launch NA effected by aperture

A„ is determined by measuring the far-field beamwidth as a function of aperture size. A catalog is thus easily established, allowing for selection of A and A to meet the needs of the LPS launch

method. Commonly accepted tolerances on A|_ and launch NA are as follows:

A

L /d = 0.707 ± 0.05 (2-28)

^

U " Ch

"A

= 0.707 ± 0.05 (2-29)

fiber NA

where d is nominal fiber core diameter.

The launch NA called for in eq (2-29) is measured at distances considerably greater than 10 d

2 /X,

which is the usual definition of far field. The launch angle is obtained from geometry, knowing the

distance from the focal plane of L to the measurement plane and having obtained the measured beamwidth at that plane. The distance from the focal plane of L to the measurement plane is accurately

known because the detector is mounted on a micropositioner stage.

The standard cut-back technique is used to calculate fiber attenuation from the measured values

of power; see eq (1-3). An alternative technique, also based on the cut-back technique, can be used

if the fiber ends are prepared with suitable care and input alignment is carefully controlled. In this case, a short piece of the fiber under test is prepared in advance, as is the test fiber. A twofiber bed on a translation stage allows the input to be focused alternately on the short fiber and the

test fiber. The two fibers are likewise coupled to the detector so one can measure the power transmitted through the short piece or the test fiber, alternately and conveniently. The ratio of the two

readings gives attenuation, but the technique depends on good agreement in the input coupling for the

two fibers. Such agreement is especially important in low-loss fibers, for which a true cut-back

technique is preferred. In this one-fiber technique, the input end (which is the more critical end)

is unchanged in the course of the measurement. Thus, the modal power distribution established at

17
launch is the same for both measurements. The two-fiber method allows input coupling errors on two counts. First, the preparation of the two fiber ends may differ, even though slightly, allowing for

differences in input coupling loss. Second, the alignment may differ, leading to a difference, how- ever slight, of the launched modal power distribution. These two effects may be cumulative, leading

to inconsistent power readings and unreliable loss values. With the true cut-back technique, using

only a single fiber, the input coupling efficiency and modal power distribution are the same for both

test and reference fiber power measurements.

2.3 Mode Filter Launch

The purpose of defining a standard launch condition is to simulate a fiber having an equilibrium

modal power distribution. The measured attenuation will then allow prediction of the attenuation ex- pected in field installations, where long fibers are encountered and an accurate prediction of system

loss is essential. Linear addition of attenuation is crucial and will be possible only if the measured attenuation for a test fiber is based on steady-state or equilibrium conditions.

Both the LPS launch and the mode filter launch yield results that scale linearly with distance

[10]. Both launch conditions were used for attenuation measurements reported in this document.

A mode filter is a device used to select, reject, or attenuate a certain mode or modes [11]. A mode scrambler is a device for inducing mode coupling in an optical fiber [11]. Our purpose is to establish the equilibrium modal power distribution; i.e., the power distribution that prevails at the

end of the long test fiber. Whether the modes are filtered or scrambled is thus an academic question.

In fact, workers do not agree on just how the equilibrium state is established [2,12,13] or how best

to accomplish the desired end. Reference 13 indicates that modal power distribution is affected in different ways by different filters and scramblers on different fibers.

The method of the mode filter launch is based on the assumption that the relative modal power

distribution at the end of a long fiber without the mode filter is the same as it is at the end of a short reference fiber with the mode filter in place. Furthermore, the method assumes that the farfield radiation pattern is a suitable indicator of whether or not the modal power distributions are,

in fact, the same. If those patterns are the same, or nearly so, the mode filter has served its purpose, having eliminated certain modes and induced an equilibrium modal power distribution which is

equivalent to that at the end of a long fiber.

The mode filter probably does more than just eliminate certain high-order modes. It may induce

mode coupling as well, to establish a balance between intermodal power transfer and modal attenuation.

The primary function of the filter, however, is to eliminate the high-order modes.

The power distribution in the far field of a fiber depends on modal power distribution. If all

modes carry the same power, then each incremental area of the core cross section at the fiber end will

uniformly illuminate its cone of acceptance. Therefore, all areas on the fiber core that have a local

numerical aperture greater than sine will contribute equally to the far-field power at angle 9, where

e is the angle between the fiber optical axis and the reference point in the far field. The far-field

pattern is therefore a function of fiber numerical aperture. In practice, mode coupling and modedependent loss lead to unequal power distribution among the modes at the output end of the fiber. In that case, not all modes contribute equally to the power at angle e. Nevertheless, the far-field

18
pattern width is still a measure of fiber numerical aperture, although the specification of how

pattern width is defined now becomes a consideration.

In the mode filter method, the adequacy of the mode filter is based on a comparison of the farfield patterns of two fibers (the test fiber without a filter and the reference fiber with the

filter). If the angles agree at the 5 percent intensity points, modal power distribution is assumed

to be approximately the same.

The mode filter is qualified as follows. Power is launched into the long test fiber with a spot

size greater than the fiber core size and with launch numerical aperture greater than the fiber

numerical aperture. This will be refered to as overfilling the fiber. The far-field radiation

pattern is then measured, where far field means distances greater than 10 d

2 /X from the fiber end, and

where d is fiber core diameter. A short reference fiber is then prepared for the purpose of

"qualifying" the mode filter. The reference fiber is overfilled and then subjected to the mode

filter. The far-field radiation pattern of this reference fiber is measured and the mode filter is adjusted to produce a far-field pattern which is equivalent (within tolerance) to the pattern of the

long fiber without the filter. The filter is deemed acceptable if the pattern widths are the same at the 5 percent intensity points. The tolerance is given below [eq (2-30)].

The procedure uses the arrangement shown in figure 2-9 [15]. A filter is normally qualified for

only one fiber. Changing the test fiber usually calls for a change (even though slight, in some cases) in the filter. Once the filter has been qualified, attenuation is measured using simple launch

optics. The fiber is overfilled and the filter is in place for power measurements on both the long test fiber and the short reference fiber, to insure that the insertion loss of the filter is accounted

for.

Workers have used several forms of mode filter, including dummy fibers, macroscopic-bend mandrel

wraps and serpentine bends [16], The measurements reported in this document were taken with a serpentine bend filter, which is shown schematically in figure 2-10. This design is similar to that

used by other workers [17], The filter consists of 7 nylon posts, each of 1 cm diameter. The posts

are on 1.3 cm centers. Three of the posts are on a translation stage, allowing for movement of those

posts to adjust the strength of the filtering.

LONG TEST LENGTH

V

/

OVERFILL MODE

FILTER

REFERENCE V

LENGTH ^/

9 S~ e L -3 ±3%

Figure 2-9. Arrangement for qualifying a mode filter.

19
FIBER

1.3 cm

NYLON POST

1 cm DIA. Figure 2-10. Mode filter used for measure- ments reported herein.

The mode filter technique requires knowledge of 9 L (see fig. 2-9); e

s is then measured using a short length of reference fiber taken from the spool of test fiber. Moving the posts of the filter

(fig. 2-10) changes the angle 9

S

. The requirement is [18] "

AG =

L -0.03 ± 0.03. (2-30)

The equation is defined so A6 is not positive. A negative value for A6 results from excessive

filtering. In that case, the mode filter causes 6

S to be slightly smaller than (or, at most, equal

to) 0|_. Equation (2-30) discourages the acceptance of high-order modes that are known to lead to inaccurate loss measurements. A positive value of A6 implies inadequate mode filtering.

The experimental arrangement for the mode filter launch is simpler than that for the LPS launch

because careful control of the spot size and launch numerical aperture are not required. The fiber

must be overfilled and this is easily accomplished without much fuss. A typical experimental

arrangement is shown in figure 2-11, where the mode filter is shown as a mandrel wrap [10]. The

attenuation measurement technique is as follows (cf. fig. 2-11): After the filter is qualified, it is used in the long test fiber and detector power is measured. The fiber is then cut as shown in the

figure and power is measured out of the cut length under the same launch conditions. The ratio of the

two powers provides the loss using the cut-back formulas.

:Q>

X- Q

•Cut Length"

a

Detector

Test FiberFigure 2-11. Experiment arrangement for attenuation measurement using a mandrel wrap mode filter [12].

20
That the mode filter launch and the LPS launch should yield comparable loss measurements is not obvious. It seems intuitive that different amounts of power are coupled into the test fiber under the

two launch conditions. Furthermore, the LPS launch is based on both near field (launch spot size) and

far field (launch numerical aperture) information. The mode filter launch is based entirely on the

far field. A question naturally arises then as to whether one can expect the two methods to establish

equivalent modal power distributions in the fiber. Most important in this regard is the attenuation

or elimination of high order and leaky modes. Either method is effective in this regard. Beyond

that, however, we are forced to conjecture on the similarities of the two methods. Figure 2-6a is

useful in visualizing concepts. The darkened area is proportional to power launched under the LPS method. That area represents the product of physical area and angle, as already discussed. According

to eq (2-27d), the ratio of power carried by a fully filled fiber (including leaky modes) to that

carried by a fiber filled at the 70/70 level (PjOT^LPs) is 2 ' 67 or 4 * 26 dB * If a mode filter

eliminates the leaky modes from the filled fiber, the ratio reduces to 3 dB L~(P|_ps + ^d^LPS-'*

Thus, the ratio of power launched into an overfilled test fiber with a mode filter to that launched

using the LPS method is 3 dB or possibly less. If the mode filter introduces additional loss (which

is assuredly the case), the figure will be less than 3 dB.

The mode filter almost certainly does more than just eliminate the leaky rays. It probably

attenuates the high-order modes and encourages modal power coupling as well. This seems obvious from

the fact that the filter must restrict the far-field pattern of the fiber in order to be acceptable.

It seems reasonable, then, to suppose that the mode filter eliminates power associated with the

following regions of figure 2-6a:

°- 5 < (77r4-)

2 < 1 " ( r / a ) 2 (2" 31 )

and

k sin 9 c

i - (r/a)

2

< (|f^-)

2

< 1. (2-32;

sin tt c

If so, the ratio of power launched with a mode filter to that launched using LPS is (P[_p5 + p

<j)/ p

|_PS or 1.76 dB (see eq (2-27e)). This assumes that the filter does not attenuate low-angle rays. It further assumes that the rays specified by eqs (2-31) and (2-32) are completely eliminated. A laboratory measurement of power launched into a fiber using the mode filter and the LPS launch yielded

a ratio of 1.64 dB.

If what we suggest here is true, then the two launch conditions will yield comparable loss

measurements even in fibers having differential mode attenuation. If a fiber has very little

differential mode attenuation, the two methods will yield comparable results even if what we suggest

is not true.

Appendix A relates these concepts to the fiber mode volume. The latter term is a popular one that is easy to understand since it identifies the number of modes that a fiber can support.

Appendix A shows that the ratio of the total number of guided modes supported by a parabolic fiber to the number supported between r = and r = a/72, is 1.25 dB. Thus, the preceding discussion suggests

that the mode filter may eliminate all of the leaky modes but couples some of the energy into loworder guided modes.

21
3. Component and System Variabilities

The measurement system shown in figure 2-8 will yield meaningful results only if the conditions

of the restricted launch (either LPS or mode filter) are met. That they are met is confirmed through

measurement. The variabilities encountered in measuring the pertinent parameters are discussed in this section. In addition, linearity and noise are discussed for the dynamic range and wavelength

range of interest in the current telecommunications-grade fiber market.

The measurement of magnification (denoted m and discussed in the following section) allows a prediction of launch spot size for a known aperture size A . The measurement of m and of launch

numerical aperture require the measurement of beam widths. Unfortunately, there are fundamental

limits to the accuracy with which one can measure those widths. The limits are imposed by virtue of

diffraction and the finite size of the detector aperture.

A similar limit is imposed in qualifying the mode filter. The patterns being measured invariably

have sloping skirts which make it difficult to clearly define the 5 percent points of the pattern.

This section also addresses the question of component and system linearity and system noise. For fibers of interest today, the required dynamic range is only a few decibels so acceptable linearity is

easily attained. System noise is well below the level of tolerance.

3.1 Spot Size and Launch Numerical Aperture

Independent adjustment of launch spot size and launch numerical aperture is accomplished using

apertures A and A of figure 2-8. The diameter of the spot focused onto the end of the fiber is the

magnified diameter of A , where the magnification m is approximately

m = f H (3-1)

3

where i is the distance from A to L and f is the focal length of L . Although m is defined here in

terms of distances, in practice it is experimentally determined since l is not known accurately, m is found by measuring the launch spot size (mA^ using a large aperture. The variation of m with

wavelength is shown later. The diameter of A is determined by visual examination using a microscope

with a two-dimensional vernier stage to identify edge location.

Measurement of m is accomplished by placing a small aperture in front of a detector and in the

image plane of L . The combination is scanned across a diameter in that plane to determine spot

size. Knowing the size of A, then allows the calculation of m.

l

If the focused image of the aperture had spot has perfectly sharp edges, sweeping the detector

aperture through that spot could be described by the convolution of two cylinder functions

CYL(r/d

s

) * CYL(r/d

a

), as shown in figure 3-1, where

1 , < r < d/2

CYL(r/d) = 1/2, r = d/2 (3-2)

, r > d/2

where d and d are the diameter of the spot and the aperture and * denotes convolution.

22
Figure 3-1. Two cylinder functions, representing an aperture and a spot

being measured.

The cylinder function is an accurate description of the transmittance of the circular aperture

over the detector but the focused spot invariably has skirts, owing to diffraction. Nevertheless, it

is instructive to consider the case of perfectly sharp functions to describe both the spot intensity

(in the focal plane of L ) and the aperture. To estimate potential errors encountered in the system,

and to define the "small aperture" alluded to earlier, we consider a one-dimensional problem, the

convolution of two rectangular functions, one of width w

s and one of width w , where the subscripts

refers to spot and aperture; we take w

$

> w

g

. The functions and their convolution are shown in figure 3-2. This figure shows that the accurate measurement of w

$ is difficult. The measured form

(fig. 3-2c) differs from the actual spot (fig. 3-2a) by an amount that depends on w

a

. The FWHM of

figure 3-2c differs from that of figure 3-2a by w

a

.

Clearly, we require w

a << w$

. If w

a is a delta function, the spot is reproduced exactly in the

measurement. However, as w is decreased to improve the measurement precision, the signal-to-noise

ratio is decreased. Obviously, the measurement of launch spot size calls for a compromise in the name

of accuracy, w should be as small as possible, commensurate with the need for acceptable signal-tonoise ratio.

Since total measured width is proportional to w

a + w

s

, the allowed value of w

a is proportional to allowed error on measured w_. For 1 percent error, w

a must be not more than 1 percent of w$

. If the

spot size is defined at the 10 percent intensity points, w

a can be slightly larger: wa

< 0.0125 w

$

. The convolution suggested by figure 3-1 does not differ substantially from that shown in figure 3-2,

if d, « d c

. a S

This simple approach, based on rectangular functions in one spatial dimension, is useful because

it is intuitive. In practice, the measured spot is the convolution of a cylinder function and a twodimensional function which accounts for diffraction.

23
g(x)

k

!a) (b)

f(x) *g (x)

(c)

Figure 3-2. The convolution of two rectangulr functions, illustrating the error introduced when

measuring f(x) (a) using an aperture g(x) (b) resulting in f(x) * g(x) as shown in (c).

Figure 3-3 shows the measured spot in the focal plane of L with A = 3012 ym at 850 nm, with a

1 ym aperture over the detector. The width at the 10 percent intensity points is 140 ym, indicating

that

m = 1/21.6. (3-3)

Figure 3-4 shows how magnification changes with operating wavelength. Obviously, the chromatic

aberrations of the intervening lenses and the beamsplitter are not excessive. Variation of m over the

range measured is ±0.1 or about 0.5 percent. If the fiber core diameter is 50 ym, the launch spot

size should be 35 ym. Invoking the ±5 percent allowance on spot size yields

702 ym < A < 810 ym. (3-4)

To determine spot size, the vernier of the translation stage that holds the detector is read at the appropriate signal levels.

The magnification is not expected to change with LNA. The accuracy with which one can measure

spot size, however, is a function of the size of A (LNA). Figure 3-5 shows measured values of m as a function of the f-number of the lens L . This variation is due primarily to loss of resolution.

The method used to determine LNA can be described with the help of figure 3-6. The source image

refered to in the figure is the image of aperture A . The source image is in the image plane of L_. A plane at distance Z from the source image is in the far field of that image plane.

24
S 219

Figure 3-3. Measured spot in the focal plane of L.

850 900 950

Wavelength, nanometers

1050

f*

Figure 3-4. Change of demagnification with wavelength. Figure 3-5. Change of demagnification

with f# (aperture size).

25
Figure 3-6. Geometry and angles encountered in measuring LNA.

Launch numerical aperture is calculated from the pattern width in the far-field plane and the

value of I. The pattern width is measured by placing a small aperture in front of a detector and

sweeping the combination in the plane at distance I from the source image.

The pattern measurement is difficult because the edges are not sharp and the corners are rounded. One source of distortion of the pattern is a (cose) 1* variation owing to simple geometry, as follows. Assume that the radiance at the source image is N. The incremental power at ds ' , in the far

field, is

dP = N ds cose dfi, (3-5)

where

da

ds' cose

(Jt/cose) 2

' (3-6)

Taki ng

^1 = constant for e < 6. . Ift o LNA

for e > 'LNA

dP

N ds ds' (cose) 1* o (3-7)

For I large with respect to source image, the power pattern seen by a pinhole detector is then

26
P = P (COS! '3-i

where P Q is the on-axis value, which depends on N Q

, I, and source size. The pattern is invariably

rounded at the edges, because of this (cose) 4 function [19]. For small values of LNA, a binomial

expansion of (cose) 4 yields an expression for P(y)/P(0), where y is the rectangular coordinate

perpendicular to the optical axis in the plane of measurement:

P(y)

P(0)

1

i + [if

(3-9;

The maximum value of y/i of interest is y n /£ o'y— = tan(sin _1 LNA' (3-10)

For LNA = 0.2, P(y

o )/P(0) is 0.92 at the edge of the pattern, as shown in figure 3-7. The pattern

measured is further distorted because of the finite size of s ( f ig. 3-8), which causes the skirt shown

in figure 3-7. The far-field criterion is therefore

l »

S'lna: (3-n

For a fiber having a 50 ym core diameter and 0.2 numerical aperture,

is required.

£ » 125 ym

cosH

Variation

(Not to Scale)

Figure 3-7. Illustrating the distortion of the pattern edge

owing to the (cose) 4 variation.

Figure 3-8. Showing the geometry and angles which cause

the skirt shown in figure 3-7.

27
Table 3.1.

f/# or Pattern width LNA aperture at 10% points

diameter (mm)

d

f/# = 1.4 3.72 0.34

f/# = 2.0 2.67 0.25

f/# = 2.8 1.95 0.19

f/# = 4.0 1.41 0.14

d = 3.13 mm 1.42 0.14

d = 6.23 mm 2.89 0.27

Table 3.1 gives the measured values of LNA taken 5 mm from the focal plane. LNA can be changed

by changing either the iris diaphragm of the lens L or by placing an aperture in front of L_ with its

diaphragm open. Both techniques were used. The lens diaphragm consists of leaves which mesh together

to only approximate a circular aperture. The aperture placed in front of the lens is circular.

However, there was no discernable difference in the far-field patterns of the two openings.

The first column of table 3.1 gives the f-number setting of the lens when the lens diaphragm was

used to restrict LNA. Lens L has a 12.5 mm focal length. When the f-number setting is 4, then, the

diaphragm opening is 3.13 mm. The fourth and fifth rows of the table should be the same. The

measured values of LNA do agree to within the measurement precision.

Arbitrary values of LNA can be obtained by adjusting the iris diaphragm on L . This was verified

by requiring and obtaining LNA = 0.22. The technique is based on the fact that LNA varies linearly

with aperture A if the angles are small. In this case, the widths given in table 3.1 were used as the starting points. The aperture was adjusted while observing the intensity on a strip chart

recorder. Proportional change of pattern width yielded a proportional change of LNA.

Measurements verify that LNA is independent of spot size. There was no discernable difference in

measured LNA for a three-fold change of spot size.

3.2 Mode Filter Qualification

Figures 3-9 and 3-10 show the launch optics and the measurement apparatus used to qualify the

mode filter used in the attenuation measurements [20]. A broadband interference filter is used

(fig. 3-9) to improve signal-to-noise ratio. The 10 nm filters used in the attenuation measurement do not provide adequate signal level for reliable measurements; the filter used here has an approximately

80 nm spectral linewidth. The measurements are relatively insensitive to wavelength, so the increased

linewidth does not affect the interpretation of results. More will be said of this later. Aperture 1 determines launch spot size and aperture 2 controls LNA, as before. The fiber is overfilled for these

measurements so the launch conditions are not critical. Alignment is straightforward and based on the

criterion of maximum signal. The chopper frequency is set at about 45 Hz. The pattern is measured by

using a fixed fiber end and a detector that moves along an arc about the center of the fiber end.

The fiber passes through a cladding mode stripper consisting of two 10-cm long felt pads wetted

with index-matching fluid. Any buffer coatings are removed from this part of the fiber. Near-field

scans have shown that this type of mode stripper effectively removes light from the cladding.

28
CHOPPER

WHEEL

RADIATION ^ FROM >h- INCANDESCENT—*"

LAMP s*

BROAD BAND

INTERFERENCE

FILTER

APERTURE

NO. 1

LAUNCH

LENS

;uTRANSLATION — c

FIBER ?

APERTURE

NO. 2

Figure 3-9. Launch apparatus used to measure near field and far field of fiber.

A vee groove positions the fiber to be coincident with the axis of rotation. A small, feltpadded weight holds the fiber in the groove. Before measurement, the fiber end is visually inspected

for flatness and perpendicularity. The vee-groove position can be adjusted by a two-dimensional

translation stage to assure proper alignment.

Scanning is accomplished with a stepper-motor-controled rotary table, which swings the detector

through a 12-cm radius arc. At this distance the far-field criteria is satisfied for core diameters

of 100 pm or less. Angular motion (1/2 arc min per step) is fine enough to give smooth far-field

curves. Detector aperture size is chosen to give reasonable compromise between resolution and signalto-noise ratio; the 0.8 mm diameter aperture gives a resolution of 0.38°. A simple one-dimensional

model based on a parabolic-shaped far-field pattern with an NA of 0.2 predicts an error of 1.6 percent

in radiation angle when the curve is acquired with 0.38° resolution. Measurement precision for

determining radiation angle is in the range of 1 to 2 percent when a new output end is prepared and

realigned; therefore, a reduction in aperture size would not result in much improvement.

CLADDING

MODE STRIPPER

PIN SILICON DETECTOR

APERTURE

TO LOCK-IN AMPLIFIER

FIBER

STEPPER MOTOR

CONTROLLED ROTARY TABLE

Figure 3-10. Apparatus used to measure fiber far field. The fiber end is fixed and

the detector moves along an arc.

29
Figure 3-11. Far-field pattern of test

fiber 7502 at 850 nm.

Figure 3-12. Far-field pattern of reference fiber 7502 with mode

filter at 850 nm (left) and 1060 (right).

A silicon PIN diode operating in the photovoltaic mode is used as the detector. The detector has

an active area of 5.1 mm2 and a built-in operational amplifier, and is mounted directly behind the

aperture. A time constant of 0.4 s is used on the lock-in amplifier. The scanning rate is chosen so one resolution element (0.38°) is scanned in approximately three time constants. At this rate, a farfield pattern is obtained in 3 to 4 min.

The output numerical aperture of a fiber is relatively insensitive to wavelength [21] for the

range of interest here. Insofar as this is true, the mode filter need not be requalified for a change

of wavelength. To verify this important assumption, a mode filter was qualified at 850 nm and then

tested at 1060 nm. The resulting far-field patterns are shown in figures 3-11 and 3-12. There is virtually no difference in the pattern widths. Unfortunately, the signal-to-noise ratio decreases at 1060 nm, making the graph more difficult to read.

If the differential mode attenuation changes with wavelength, the far-field pattern is a function

of wavelength. Indeed, any change in the modal power distribution will produce a change in the farfield pattern. If the differential mode attenuation (DMA) is a function of wavelength, a mode filter

that is adequate at 850 nm, may not be so at 1300 nm.

30
Table 3.2.

Indicated fullscale voltage 1000 1000//10 100 100//10 10 10/710 1

Measured fullscale voltage 1000 317.2 100.3 31.71 10.03 3.165 0.992

(1000 mV range

as reference) ±0.01 ±0.01

Offset (%) 0.3 0.3 0.3 0.3 0.1 0.8

3.3 Component Linearity

Potential nonlinearities exist at the detector and at the lock-in amplifier/digital voltmeter.

Because the reference detector and electronics operate at essentially the same signal levels during

measurements on the long and short fibers, nonlinearities in those devices are not likely.

Silicon PIN photodiodes are generally found to be linear at power levels of interest (< 10 yW

total power). The silicon device used here had previously been calibrated against a calorimetric

standard at 1 yW and 1 mW with an apparent difference in responsivity of not more than 0.8 percent.

The linearity of the lock-in amplifier/digital voltmeter combination was determined by comparison

with a precision inductive voltage divider. The scale factor for individual scales was constant to

0.1 percent (peak to peak) or better from 3 to 100 percent of full scale for each of the scales most

often used, increasing to about 0.9 percent (peak to peak) for the most sensitive scale used and to 3 percent for the most sensitive scale on the instrument. Relative offsets between ranges were also

measured and are shown in table 3.2.

This offset error can be avoided by making both measurements on the same scale. A slight adjustment of light power, for example, is often all that is required to insure that a scale change is not required. For our lock-in amplifier, the error encountered in the scale change is about 0.3 percent over most of the range.

3.4 System Linearity

The linearity of the system is most likely to degrade at high intensity points, if at all. System linearity was tested through judicious use of neutral density filters and adjustment of power out

of the light source. The test was conducted using narrowband (10 nm) filters to avoid variabilities

introduced through the spectrum shift when intensity of the light source was changed. The technique

used was as follows: First, a short length of fiber was used to transmit power to the detector. A 2.5 dB filter was then inserted into the launch optics. Attenuation was measured as 2.50 dB. The

filter was removed after noting the reading of the DVM (digital voltmeter). The intensity of the

light source was then reduced by 2.5 dB so the DVM reading was the same without the filter as it was just before the filter was removed. This represents a new reference reading and the procedure was repeated. The process continues until signal-to-noise ratio is reduced to intolerable limits.

The underlying assumption in this approach is that the attenuation of the filter is independent

of power level. Since only relatively low power levels are used, this assumption is reasonable but no

31
attempt was made to verify it. The measurements were made without changing the scale of the lock-in

amplifier. At 850 nm and over a dynamic range of 15 dB, the standard deviation of the filter loss was

0.01 dB or 0.4 percent. The results were confirmed at several wavelengths of interest. The system

linearity at 1300 nm was tested over only about 7 dB of dynamic range but the results were the same.

3.5 System Noise

System noise contributes to measurement imprecision, but the level of such noise is usually low.

Analysis of the expected noise follows [22]. We adopt the following notation:

A = measured fiber attenuation, dB

V,M = voltage levels at the output of the fiber and the light source monitor, respectively

S(«) = standard deviation

subscript s, £ = short and long fibers, respectively.

In terms of V and M, attenuation is

V /M

A = 10 log tiTTM

1

] ( 3 - 12 )

and

S(V ) S(M ) S(A) = 4.34[(-

1

i-) 2 + {-^-f

s s

+ (——) + (—pj—] ] • (3-13)

£ £ Digitizing noise in the five digit DVM establishes a level of about 10-lt for each of the ratios

S(V

S )/VS

, S(M

S )/M

S

, S(V

£ )/V r

S(M£ )/Mr

Hence,

S(A) = 0.001 dB. (3-14)

For high-loss fibers, S(V £ )/V„ may limit the dynamic range of the system. Experience has shown,

however, that such a limit is not a practical problem since telecommunication-grade fibers of interest

seldom have attenuation of more than 3 to 5 dB/km.

Measurement of fibers in the laboratory yielded the following values

sm m~

5 x 10

_

3 at x

= 1300 nm>

V M

^p-, ^1 < 5 x 10 _t+ at \ = 850 nm.

The system noise contribution to the standard deviation of the attenuation measurement is therefore

about 0.001 dB at 850 nm and 0.01 dB at 1300 nm.

32
(a) (b)

Figure 3-13. Response of silicon (a) and germanium (b) detectors.

3.6 Detector Uniformity

Figures 3-13(a) and (b) show detector response over the surface of the detector. Figure 3-13(a)

is silicon; figure 3-13(b) is germanium. The silicon detector exhibits uniform response, even at its

edges. The germanium is uniform over the central region of its surface, but not at the edges. Use of

the germanium detector therefore requires more care than does the silicon one. Avoiding the edge is only a minor invonvenience and presents no technical problems. In each case, the detector surface is about 1 cm diameter.

3.7 Measurement Procedure

The cut-back method of measuring attenuation is based on eq (1-3); it calls for the measurement

of relative power transmitted through two lengths of the fiber under test. In the notation of

eq (1-3), we use L to refer to a short length (the reference length) of the fiber under test; L is the full length of test fiber. The measurement can be performed in either of two ways. To distinguish, we will refer to the first as the two-fiber method; it is suitable for measuring attenuations

of more than about 4 to 5 dB. In the two-fiber method, length L is obtained, in advance of any measurements, from the test fiber. Both fibers are prepared and the two input ends are placed on a translatable bed, allowing the light source to be coupled alternatively to length L Q or L , as appropriate.

Both output ends are likewise coupled to the detector by placing them side by side on a bed that

allows equivalent coupling conditions between the fiber and the detector. In this procedure, care

must be taken to ensure that the input ends of the fiber are of similar quality. Input coupling loss

can vary, leading to unreliable results if such care is not taken.

In the cut-back method, power transmitted through length L is measured. Without disturbing the

launch conditions, the fiber is cut at a point about 2 m from the input, thereby obtaining the reference fiber of length L . The cut end is prepared and the power transmitted through L is measured.

Equation (3-1) is used in either case to obtain attenuation.

33
Carbide -Tipped

Blade

Brass Bed

Radius of Curvature

3.2 cm

Rubber Based

Holding Clamp

Figure 3-14. Method of cleaving the fiber.

Each of the methods has advantages and disadvantages. The cut-back procedure insures that the

long and short lengths are excited with identical launching conditions and also involves the

preparation of three rather than four high-quality end surfaces. It therefore is expected to yield

better precision, especially with low-loss fibers. The two-fiber procedure, on the other hand,

facilitates repeated measurements.

Systematic tests were conducted to determine the sacrifice in precision suffered in using the

two-fiber method. The method may introduce as much as 0.1 dB variation in the measured attenuation

unless extreme care is taken in preparing the input ends. Only then will input coupling loss be the

same for the two fibers. The cut-back method introduces less than 0.03 dB variation in measured

attenuation. The output coupling loss is small and is not sensitive to the quality of the cleave, at least if the cleave is reasonably good.

For either measurement method, about 10 cm of bare fiber is required on both ends to accommodate

mode strippers. Fiber ends are prepared by scribing with a hand-held silicon carbide razor blade

while the fiber is under tension. The method is shown in figure 3-14.

Cleaved ends are visually inspected for acceptability with both a 40 power and a 100 power

microscope having NA = 0.12 and 0.25. Acceptance is based on a subjective evaluation of smoothness

without hackle, lips, breakover or deep notches at the point of scribing, and perpendicularity. Glass

chips or foreign material (dirt, jacketing material, etc.) adhering to the end are removed with

adhesive tape.

Visual inspection with only one orientation can be deceptive. For this reason, the ends are examined from different angles and under different types of illumination.

The input end is mounted on the x-y-z positioner with the mode stripper in place. The launch

spot and the fiber end is viewed for alignment with the vidicon and monitor. The fiber output ends

are taped to a flat surface in front of the detector so the axes of the two fibers, if extended, would

intersect at the surface of the large area detector. Care is taken to ensure that all the power out

of the fiber is collected by the detector.

With the source aperture in place, the appropriate diaphragm set at the launch lens, and the

filter wheel set, the positioner is adjusted to place the input face of the fiber at image plane of

L . Minor axial repositioning to maximize transmitted power is done at each wavelength. When small

34
CHOPPED

LIGHT SOURCE

Monitor

Text

FIBER

DETECTOR DETECTOR

LOCK-IN

AMPLIFIER CHOPPER REFERENCE

LOCK-IN

AMPLIFIER

DVN CHART RECORDER DVM

BCD

INTERFACE BCDINTERFACE

DESK-TOP COMPUTER

OPERATOR

Figure 3-15. Block diagram of measurement configuration.

input spot sizes are used other position criteria may be used. Increasing LNA to improve focusing

resolution is sometimes useful.

The lock-in amplifier scale is selected on the basis of expected attenuation and the need to avoid scale change, if possible. The amplifier meter in our case has a decibel scale which can be

used to assist in this regard. In so doing, recall that the scale measures electrical power, not volts; thus, 2 dB optical loss will be reflected as 4 dB on the electrical scale.

Figure 3-15 is a block diagram of the configuration. The operator is offered three options in the course of taking data. Each option is offered by a screen prompt followed by a computer pause.

The operator must respond before the program will proceed. First, the option of monitoring the light source for drift is offered. Experience has shown that a stabilized power supply eliminates drift, so monitoring the source is not often required. If the source is monitored, a correction for drift is imposed in calculating attenuation. The correction is normally small.

Second, the operator is asked to specify the number of data points taken and the time (in

milliseconds) between readings. The selected pause between readings is based on the time constant of

the lock-in amplifier. The readings must, of course, be independent, which requires that several time

35
Table 3.3.

Fiber Wavelength Method* Number Average Standard

idenfication (nm) of attenuation deviation

measurements (dB) (dB)

4103 850 MF 5 2.81 0.05

4103 850 LPS 5 2.75 0.04

4103 1300 MF 3 1.62 0.04

4103 1300 LPS 2 1.65 0.02

5202 850 MF 4 1.98 0.09

5202 850 LPS 3 2.18 0.04

5202 1300 MF 3 1.03 0.01

5202 1300 LPS 3 0.92 0.02

7502 850 MF 5 5.83 0.07

7502 850 LPS 2 5.61 0.01

7502 1300 MF 6 1.85 0.05

7502 1300 LPS 3 1.59 0.01

*MF = mode filter; LPS = limited phase space

Test Fiber

Reference

Fiber with Mode Filter

Figure 3-16. Typical far-field pattern of test fiber and

reference fiber with mode filter at 850 nm.

36
constants elapse between readings. It is sometimes true that the signal-to-noise ratio depends on the

number of time constants between readings. If so, the selected pause is adjusted accordingly. The

average reading and the standard deviation of the readings reach steady state after about 25 readings.

Typically, 30 to 50 readings are taken for each measurement. The additional time consumed by taking

50 data points rather than 30 is small and leads to more confidence in the results.

3.8 Some Results

Measurement results are presented here for three telecommunication-grade fibers. Attenuation was measured at 850 nm and 1300 nm. The mode filter was qualified only at 850 nm for each fiber. Figure

3-16 shows the far-field patterns taken for one of the fibers. These plots are typical of those seen

by the system being used here. Table 3.3 gives the results of the measurements of the three fibers;

the measurement precision is +0.1 dB.

The data show no clear indication of one launch condition yielding attenuation values consistently lower or higher than the other. The greatest difference encountered is about 0.3 dB on fiber

7502 at 1300 nm. In that case, the mode filter launch yields attenuation that is higher than that

found using the LPS launch. Fiber 4103 has nominal length of 0.97 km, fiber 5202 is about 1.1 km long

and fiber 7502 is about 2.2 km. The data for fiber 5202 was taken using a mixture of the cut-back and

the two-fiber methods. The data show that the standard deviation was not adversely affected in going

from one method to the other.

4. Measurement Comparisons and Results

The procedures discussed in this document have evolved over several years; they are based on the

desire to define techniques that lead to usable and realistic predictions of attenuation in long fiber

links. The procedures described are approved and sanctioned by the EIA (Electronics Industries Association), who drafted them and guided them through the approval stage.

A comprehensive interlaboratory comparison was conducted during 1980 to establish confidence and

provide a definitive evaluation of the EIA procedure [23]. In the following, we discuss that interlaboratory test. The material presented here is exerpted from reference 23.

4.1 Participants and Instructions

The participants in the interlaboratory comparison included NBS and nine vendors who are members

of the EIA. These included most US and some Canadian manufacturers of fiber or fiber cable. Participants were given a brief description of the physical characteristics (manufacturer's specifications)

of the test fibers and special handling instructions. The following instructions were given.

For mode filter launch:

1. Overfill the test fiber in both spot size and numerical aperture, then measure the long fiber

far-field radiation pattern and determine 9 , the full width at the 5 percent intensity points.

2. Apply a mode filter to the test fiber and adjust until the far-field radiation pattern at the 5 percent intensity points from a 1.8 m length is 9 with a tolerance of +0, -7 percent (the current tolerance is -3 ± 3 percent). This procedure qualifies the mode filter for the attenuation measurement.

37
3. Apply the same mode filter to the test fiber, then measure the attenuation (mode filter is in place and undisturbed for both long and short length measurements) using a reference (cutback)

length of 1.8 ± 0.1 m and some type of cladding mode stripper.

For LPS launch:

1. Use beam optics to produce a launch spot with a diameter at the 50 percent intensity points of

70 ± 5 percent of the core diameter.

2. The launch numerical aperture determined at the 5 percent intensity points shall be 70 ± 5 percent of the fiber numerical aperture.

3. Use manufacturer's numbers for core size and MA.

4. The launch spot shall be centered on the fiber core.

5. Attenuation shall be measured using a reference length of 1.8 ± 0.1 m and some type of cladding

mode stripper.

In addition to a test of the restricted launch conditions, the interlaboratory tests provided an opportunity to compare the results with those obtained using an overfilled launch condition. This

provided additional insight into the effect of the two launch conditions on measured attenuation. The

participants were asked to measure attenuation using overfill conditions, according to the following

instructions.

Overfilled Launch:

1. Use a launch spot size which overfills the fiber core.

2. Use a launch numerical aperture of 0.24 or the next larger size available to you.

3. In making the measurement, use a reference (cutback) length of 1.8 t 0.1 ra and some type of

cladding mode stripper.

The test fiber parameters are given in table 4.1.

4.2 Comparison Results

This interlaboratory comparison yielded data on the stability of fibers that are subjected to repeated handling and shipping. The fibers were returned to NBS and remeasured after each participant's measurement, to identify trends. One of the four fibers (fiber B) tended toward decreasing

attenuation so it was retired after five participants. The one standard deviation spread for fibers

A, B, C, and D was 0.06, 0.10, 0.08, and 0.10 dB/km; precision of the NBS measurement system was typically 0.1 dB/km at 850 nm, the wavelength of interest in this comparison test.

Each participant was told the fiber length and results were reported in dB/km. Participants

typically used 10 m of fiber to complete all measurements and were requested to use no more fiber than

needed to make two measurements of each quantity. NBS monitored the fiber length so results could be given in dB/km.

Attenuation results from 10 participants are summarized in figures 4-1 through 4-4, table 4.2,

and table 4.3. A few reported values were clearly outside the dominant distributions. Of 60 reported

38
Table 4.1. Nominal properties of comparison fibers

Cladding Core Buffer coating Numerical Reel Length,

Fiber O.D. , pm dia. , ym thickness, pm aperture dia.

,

cm km

A 125 60 170 0.24 26 2

B 125 50 70 0.16 32 2

C 125 60 70 0.18 22 2

D 125 60 thin

polymer

0.20 30 0.9

fibers. Average system precision for the ten participants is 0.15 dB/km. One standard deviation measurement spread is 0.24, 0.11, 0.12, and 0.43 dB/km for fibers A, B, C, and D; the average is 0.23

dB/km. Approximately two-thirds of the participants used the mode filter procedure; the remainder

chose the LPS method. Mode filters included mandrel wraps, serpentine bends, and a dummy fiber. The

average mode filter value minus the average beam optics value is +0.15, -0.02, -0.07, and +0.30 dB/km

for fibers A, B, C, and D. In all cases these offsets are less than one standard deviation of the

mode filter values by themselves. Therefore, systematic differences between the two approaches are too small to appear in the comparisons with a significant level of confidence. Greater differences

between the two techniques might appear in fibers which have high differential mode attenuation. The

next section gives measurement results on two fibers which have high differential mode attenuation.

These data, supplied by P. Reitz of the Corning Glass Works, indicates little systematic difference

between the two techniques (for these fibers) if the mode filter far-field pattern from the reference

length is chosen to be in the center of its allowed tolerance. (See additional comments in the following section.

)

Overfilled launch results are given in table 4.3 for the four fibers. One standard deviation is 0.39, 0.14, 0.04, and 0.47 dB/km for fibers A, B, C, and D; the average is 0.26 dB/km. Seven participants reported initially aligning the fiber under test for peak transmitted power while two placed the

fiber at the center of the launch spot; there is no significant difference between the two alignment

methods for overfilled launch conditions. An earlier comparison had a 0.6 dB/km standard deviation

[20], Also, the average of the standard deviations obtained for overfilled launching conditions,

0.26 dB/km, does not differ much from the 0.23 dB/km resulting from the restricted launch.

Participants did significantly better on some fibers than on others. This may be due to differences in the DMA (differential mode attenuation) for the fibers. The smallest measurement spread is for fiber C, which exhibits almost no differential mode attenuation. The difference between overfilled and restricted launch attenuations is a measure of differential mode attenuation in a fiber;

differences for the four fibers in ascending order are 0.03, 0.28, 0.42, and 0.80 dB/km for fibers C,

B, A, and D, respectively. This same order occurs when fibers are listed according to increasing

measurement spread. The attenuation in high DMA fibers is more sensitive to launching conditions.

Fiber D has a high OH" concentration. The proximity of the 875 nm OH" absorption line to the 850

nm measurement wavelength may have affected the results. For example, the slope of the spectral at- tenuation for fiber D at 860 nm is +0.06 dB/nm, whereas when loss is limited by a Rayleigh scattering

as in C, the same slope is -0.01 dB/nm. A small positive offset from the measurement wavelength in

addition to a broad source linewidth would result in a higher measured attenuation (fig. 4-5) (some

participants reported using 20 nm source linewidths).

39
MSTMCTEO LAUNCH ATTtMUATHN. FKI

A

W7 11* 12* QW AVERAGE

1»

14

HI I8*'

5"

2.7 —

24 L

I

1

I

I

Figure 4-1. Results of restricted launch attenuation measurements, fiber A.

RESTRICTED LAUNCH ATTENUATION. FIBER B

PARTICIPANT

626 *33 726 662 344 24

US

2A 5"

£0 <—

I

SAMPLE AVERAGE

I

}<

Figure 4-2. Results of restricted launch attenuation measurements, fiber B.

RESTRICTED LAUNCH ATTENUATION. FIBER C

PARTICIPANT

24

2.4 E

I 2.

HI

2J

12 -

724 133 626 344

I I

107 118 SAMPLE OH AVERAGE

I

I

2.67 d8Am i l

Figure 4-3. Results of restricted launch attenuation measurements, fiber C.

40
E 45

RESTRICTED LAUNCH ATTENUATION. FIBER O

PARTICIPANT

72» 526 344 M2 307 111

I

I

SAMPLE AVERAGE

I

I

3.W dB/km ' '

Figure 4-4. Results of restricted launch attenuation measurements, fiber D.

4.3 Attenuation Measurements in High-DMA Fibers

The largest discrepancies between the LPS or beam optics and the mode filter launch conditions

occur in fibers having high DMA. This section gives results for two 1-km fibers that have higher DMA than the comparison fibers. For these fibers, attenuation differences between overfilled and

restricted launch at 850 nm are 1.74 and 0.72 dB/km. Table 4.4 shows the difference between the LPS

and the mode filter launch implemented at the mid-point and extremes of the specified tolerance on the

match of far-field radiation patterns. Mode filters are specified from the far-field radiation angle

at the 5 percent intensity points. If 9

L is the radiation angle produced using overfilled launching

conditions to the test fiber without a mode filter, and 6

S is the radiation angle from the short

SPECTRAL ATTENUATION. FIBER

+0.i

•*«.e-

£ o -

MO

WAVELENGTH,

Figure 4-5. Spectral attenuation change with respect

to the comparison wavelength of 850 nm

for fiber D. An OH" absorption line

occurs at 875 nm.

41
Table 4.2. Restricted launch attenuation, 850 nm (dB/km)

Participant Fiber A Fiber B Fiber C Fiber D

726

833

525

344

662

307

119

129

038

902

2.91

2.87

2.93

2.80

2.65

3.41

2.8

3.19

2.7

2.44

2.38

2.41

2.31

2.15

2.51

2.77

2.55

2.49

2.40

2.72

2.6

2.5

3.77

3.40

3.56

4.15

4.6

3.8

Mean 2.92 2.34 2.57 3.89

Standard deviation 0.24 0.12 0.12 0.43

Table 4.3. Overfilled launch attenuation, 850 nm (dB/km)

Participant Fiber A Fiber B Fiber C Fiber D

726

833

525

344

662

307

119

129

038

902

3.26

3.08

3.03

3.04

3.38

3.2

3.48

3.3

4.29

2.67

2.46

2.78

2.55

2.60

2.63

2.55

2.54

2.60

2.6

2.66

2.58

4.95

4.31

4.97

4.77

5.2

3.94

Mean 3.34 2.62 2.60 4.69

Standard deviation 0.39 0.14 0.04 0.47

Table 4.4. Attenuation using mode filter and beam optics launches in two high DMA fibers at wavelengths of 850 and 1300 nm (dB/km)

Fiber #1 Fiber #2

850 nm 1300 nm

Overfilled launch 4.16 2.97

LPS launch;

70% core, 70% NA 2.42 1.11

Attenuation diffei~ence 1.74 1.86

850 nm 1300 nm

3.25

2.53

0.72

1.74

0.94

0.80

Mode filter attenuation - 70/70 beam optics attenuation for various values

of A the fractional far-field radiation angle mismatch parameter

A =

A = -3%

A = -7%

+0.16 +0.11

-0.05 -0.04

-0.27 -0.29

+0.20 +0.38

+0.03 +0.12

-0.11 -0.08

42
(reference) length with the mode filter applied, then A6 = (6 -9. )/9. . For the comparisons, the mode

filters had to produce A9 values between and -7 percent. At both 850 and 1300 nm, the mode filter

attenuation values at the tolerance extremes (0 and -7 percent) straddle the LPS values. At -3 percent, near the tolerance mid-point, attenuation values obtained by the two approaches are nearly

the same.

The results experienced in these tests may not be typical of the results from other high DMA

fibers. This is because the exact nature of DMA may be instrumental to the relationship between the

LPS and the mode filter launch. Some fibers may experience high DMA among low order modes but low DMA among high order modes. For other fibers, the converse may be true. For still other fibers, high DMA

may prevail only in the mid-range of modes. The results given in table 4.4 are not typical of the

results that would obtain under these diverse conditions.

4.4 Summary of Interlaboratory Comparisons

The results described above suggest the following:

1. Measurement agreement for attenuation has improved since the last NBS-sponsored comparisons

[24].

2. Uncabled fibers exhibit good stability as comparison fibers if proper attention is given to buffering and winding configuration.

3. Restricted and overfilled launching conditions for attenuation measurements yield similar

standard deviations on some types of graded-index fiber.

4. The LPS and mode filter launch conditions yield nearly the same attenuation on many types of

long graded-index fibers.

5. The 0.12 and 0.04 dB/km standard deviations obtained for fiber C indicate systematic

differences between participants. These arise from various non-modal effects such as failure

to strip cladding light, nonlinear detection, and incorrect wavelength. Systematic differences are near or less than the average claimed system precision of 0.15 dB/km. As DMA decreases in future high-quality fibers, measurement agreement is expected to improve.

6. Standard deviations on some fibers are near typical system precisions. Further improvements

will require better system precisions or the use of many measurements and confidence

intervals.

The authors are indebted to Dr. M. A. Holzman, Mr. A. G. Hanson, Mr. P. R. Reitz, and Dr.

A. H. Cherin for constructive comments. The discussion on phase space, in particular, was revised

after lengthy discussions with Mel Holzman. His help is sincerely appreciated. Finally, we acknowledge the gracious and expert editorial assistance of Edie DeWeese.

5. References

[1] Olshansky, R. ; Blankenship, M. G. ; Keck, D. B. Launch-dependent attenuation measurements in graded-index fibers. Second European Conference on Optical Fibre Communication, Paris; 1976.

[2] Vella, P. J.; Abe, K. ; Kapron, F. P. Precise measurement of fiber attenuation. Technical

Digest, Symposium on Optical Fiber Measurements. Nat. Bur. Stand. (U.S.) Spec. Publ. 641; 1982.

43
[3] Personick, S. D. Time dispersion in dielectric waveguides. Bell Syst. Tech. J. 50:843; 1971.

[4] Chinnock, E. L. ; Cohen, L. G. ; Holden, W. S. ; Standley, R. D.; Keck, D. B. The length

dependence of pulse spreading in the CGW-Bell-10 optical fiber. Proc. IEEE 61:1499; 1973.

[5] Keck, D. B. Spatial and temporal power transfer measurements on a low-loss optical waveguide.

Appl. Opt. 15:1882; 1974.

[6] Olshansky, R. ; Oaks, S. M. Differential mode -attenuation measurements in graded-index fibers.

Appl. Opt. 17:1830; 1978.

[7] Olshansky, R. ; Oaks, S. M. ; Keck, D. B. Measurement of differential mode attenuation in gradedindex optical waveguides. Technical Digest, Topical Meeting on Optical Fiber Transmission,

Williamsburg; Paper TuE5; 1977.

[8] Arnaud, J. A. Beam and fiber optics (chapt. 4). Academic Press: New York; 1976.

[9] Holmes, G. T. Propagation parameter measurements of optical waveguides. In Fiber Optics for

Communications and Control, SPIE Publication 224; 1980.

[10] Gallawa, R. L. On the definition of fiber numerical aperture. Electro-Optical System Design,

46; April 1982.

[11] Hanson, A. G. ; Bloom, L. R. ; Cherin, A. H. ; Day, G. W. ; Gallawa, R. L. ; Gray, E. M. ; Kao, C. ; Kapron, F. P.; Kawasaki, B. S. ; Reitz, P.; and Young, M. Optical waveguide communications

glossary. Nat. Bur. Stand. (U.S.) Handb. 140; 1982.

[12] Cherin, A. H. ; Head, E. D. ; Lovelace, C. R. ; Gardner, W. B. Selection of mandrel wrap mode

filters for optical fiber loss measurement. Fiber Integ. Opt. 4:49; 1982.

[13] Agarwal , A. K. ; Karstensen, H. ; Unrau, U. Modal behavior of various mode mixers and mode

filters for optical fiber measurements. Technical Digest, Symposium on Optical Fiber

Measurements. Nat. Bur. Stand. (U.S.) Spec. Publ. 641; 1982.

[14] Reitz, P. R. Measuring optical waveguide attenuation: The LPS method. Opt. Spectra, 48; August

1981.

[15] Franzen, D. L. ; Day, G. W. ; Gallawa, R. L. Standardizing test conditions for characterizing

fibers. Laser Focus, 103; August 1981.

[16] Technical Digest, Symposium on Optical Fiber Measurements. Nat. Bur. Stand. (U.S.) Spec. Publ.

597; 1980.

[17] Tokuda, M. ; Seikai, S. ; Yoshida, K. ; Uchida, N. Measurement of baseband frequency response of multimode fibre by using a new type of mode scrambler. Electron. Lett. 13:146; 1977.

[18] Electronics Industries Association. Light launch conditions for long length graded-index

optical fiber spectral attenuation measurement. F0TP 50; 1982.

[19] Young, M. Optics and lasers, an engineering physics approach. New York: Springer-Verlag; 1977.

[20] Kim, E. M. ; Franzen, D. L. Measurement of far-field and near-field radiation patterns from

optical fibers. Nat. Bur. Stand. (U.S.) Tech. Note 1032; 1981.

[21] Sladen, F. M. E. ; Payne, D. N. ; Adams, M. J. Definitive profile-dispersion data for germaniumdoped silica fibres over an extended wavelength range. Electron. Lett. 15:469, 1979.

[22] Mandel , John. The statistical analysis of experimental data. New York: Interscience

Publishers; 1964.

[23] Franzen, D. L. ; Day, G. W. ; Danielson, B. L. ; Chamberlain, G. E. ; Kim, E. M. Interlaboratory

measurement comparison to determine the attenuation and bandwidth of graded-index optical

fibers. Appl. Opt. 20:2412; 1981.

[24] Day, G. W. ; Chamberlain, G. E. Attenuation measurements of optical fiber waveguides: An interlaboratory comparison among manufacturers. Nat. Bur. Stand. (U.S.) NBSIR 79-1608; 1979.

44
Appendix A. Mode Volume and Limited Phase Space

This appendix is addressed to the plausibility of agreement in the measured results when using

the LPS and the mode-filter launch conditions. The LPS launch depends only on conditions at the input

face of the fiber. The mode-filter launch is based on the far-field pattern of the fiber. Nevertheless, the plausibility of agreement is discussed in section 2.3. The subject is pursued further by

examining the number of modes excited by a limited phase space launch.

The number of guided modes (M) in a heavily overmoded fiber having a power-law refractive index

profile is found by integrating the normalized wave number over the fiber core and multiplying by 2 to account for the two allowed polarization states:

M =t-7 / l> 2 (x,y) - k2) dx dy.

4it 2 (A-l)

Converting to circular cylindrical coordinates and assuming a power-law profile with profile param- eter g:

k

2 = fe2 n2[i _ 2A(r/a) g ],

A 1 (A-2)

k

2 = A2 n2[1 _ 2A],

9 A 1 (A-3)

where n is the refractive index at r = and

n(r) = n [1 - 2A(r/a) 9

] l/2 . l (A-4]

Consider the mode volume (the number of guided modes) between r = and r = u:

2a n

2

2tt u M(u) = (^-)

—^~

j / [1 - (r/a)

9

] rd*dr.

o o

(A-5)

Several special cases are of interest (V = (2ira/X)/n 2 - n|):

Case I: u = a, g

= » (step index fiber)

M = V

2 /2

(A-6)

Case II: u = a, g = 2 (parabolic profile)

M = V

2 /4

[A7'

Case III: u = a//2, g

= 2

M = (V 2 /4) • 3/4

(A-8)

Cases I and II are well known; they imply a 3 dB loss when coupling from a step-index fiber to a para- bolic profile fiber. Cases II and III are of interest to this discussion. They imply a loss of 1.25 dB in coupling a filled parabolic fiber (filled in both core size and numerical aperture) to an identical fiber through an aperture of radius a/72, using a perfect butt joint.

45
This 1.25 dB loss is consistent with the concepts of LPS. To see this, note first that leaky

modes should be ignored since they were not included in the foregoing. Consider, then, eqs (2-27):

P + P = 3/4 (1.25 dB), (A-9)

P + 2P LPS d

Which agrees with eqs (A-8) and (A-7).

46
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS TN-1060

2. Performing Organ. Report No. 3. Publication Date June 1983

4. TITLE AND SUBTITLE

Measurement of Multimode Optical Fiber Attenuation

5. AUTHOR(S)

R. L. Gallawa, G. E. Chamberlain, G. W. Day, D. L. Franzen, and M. Young

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

~2 Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

This document is one of a series which describes optical fiber measurement

capabilities at the National Bureau of Standards. We concentrate here on

the measurement of attenuation of multimode, telecommunication-grade fibers

for the wavelength range of 850 nm to 1300 nm. The document begins by discussing the need for restricted launch conditions, the most fundamental and

crucial aspect of precise attenuation measurements. The limited phase space

launch (also called the beam optics launch) and the mode filter launch are discussed. Attention then turns to the practical matter of ensuring that the

conditions of the restricted launch are met. Discussions of system noise and

system linearity are also included. The document describes measurement procedure and results obtained in the laboratory using three typical fibers.

Results are presented for the two wavelengths of current interest: 850 nm

and 1300 nm. The procedures are applicable to any wavelength, however. The

document touches briefly on the matter of monomode fibers. Finally, a summary

of the results from an interlaboratory comparison are presented to give perspective to the stability of a fiber subjected to handling and shipping.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

attenuation; attenuation measurement; fiber measurement; optical fibers;

optical waveguides.

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